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The monotonicity and critical periods of periodic waves of the φ 6 field model

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Abstract

In this paper, we study the relationship between period and energy of periodic traveling wave solutions for the φ 6 field model. The various topological phase portraits with periodic annulus are given by using standard phase portrait analytical technique. Some analytic behaviors (convexity, monotonicity and number of critical periods) of the period functions associated with periodic waves are investigated. We prove that the period function has exactly one critical period under certain conditions. Moreover, the numerical simulation is made. The results show that our theoretical analysis agrees with the numerical simulation.

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Authors and Affiliations

  1. Center of Nonlinear Science Studies, Kunming University of Science and Technology, Kunming, Yunnan, 650093, P.R. China

    Aiyong Chen & Jibin Li

  2. School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin, Guangxi, 541004, P.R. China

    Aiyong Chen & Wentao Huang

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  1. Aiyong Chen
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  2. Jibin Li
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  3. Wentao Huang
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Correspondence to Aiyong Chen.

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Chen, A., Li, J. & Huang, W. The monotonicity and critical periods of periodic waves of the φ 6 field model. Nonlinear Dyn 63, 205–215 (2011). https://doi.org/10.1007/s11071-010-9797-0

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  • DOI: https://doi.org/10.1007/s11071-010-9797-0

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